Electroboom: How Right IS Veritasium?! Don't Electrons Push Each Other??

[electrodacus]

The equation you wrote gives the amount of power for some given sail area, right? By itself it is meaningless because you don't know how much power is needed to push the vehicle along. The entirety of your theory is that at windspeed the power available is zero, and for a sail type that would be true. But it ISN'T a sail type - it is a propeller.

As I pointed out, if it is rotating there is thrust, and when the vehicle is at wind speed that thrust is still pushing. The big question is how slow the wind speed can be be (relative to the vehicle) before the thrust from the prop fails to have an effect.

Your equation doesn't go anywhere near answering that. It is just considering one part of the problem to be solved, not the entirety. If you're relying on that equation to prove your theory then you are fooling yourself.

The way wind interacts with vehicle is the same no matter the type of vehicle.
Air particles have mass (thus the air density in the equation) and those air particles will hit the vehicle and so providing their kinetic energy to vehicle thus the vehicle area that is hit by air particles is also part of the equation and then particle speed relative to vehicle is the only other value needed in the equation.

The propeller blades and vehicle body are the sail and when propeller does not rotate it is very simple to calculate the wind power available to vehicle.
If propeller will not have been connected to wheels then all available wind energy (power integrated over time) will be converted in to vehicle kinetic energy minus a bit of energy needed for friction losses.
When propeller is connected to wheels part of the wind energy available is still use to cover friction and accelerate the vehicle but also a significant part is diverted to propeller and then propeller pushes against air (this will be completely ridiculous and useless if air was not a compressible fluid) but since air is compressible the energy taken from wind at the wheels is used to create a pressure differential (basically store energy).

But this stored energy is also used at the same time just that is used at a lower rate than it is put in so you get a net energy put in storage until around vehicle speed is at 20 or 30% of the wind speed at which point you take more out of the energy storage than you still get from wind and when I say get out I men use to accelerate the vehicle (increase vehicle kinetic energy).
When vehicle speed equals wind speed there is zero power available to vehicle from wind but there is power available from the stored energy (that pressure differential).
But the power available from the storage is still only in part used to accelerate the vehicle and cover the friction loss the other significant part is put back into energy storage as wheels and propeller are still connected. 
Of course the stored energy net (pressure differential) will decrease as you take out more than you put back in. And so acceleration rate will drop until it gets to zero and from that point the vehicle will decelerate so the friction losses are provided by the vehicle stored kinetic energy meaning vehicle will start to slow down and will do so until it gets below wind speed.

So that equation is valid for any wind power vehicle.
The difference is that for a vehicle without energy storage all that power is used to accelerate the vehicle (faster acceleration).
While for a vehicle with energy storage only a part of that power accelerates the vehicle the other part is stored to be used a bit later. Since vehicle accelerates slower it spends more time in the region where high wind power is available so more energy from the wind is collected some to increase the vehicle kinetic energy and some to increase the pressure differential.
     

[gnuarm]

This conversation has gone to the dogs, but I suppose that was inevitable with the givens...

[electrodacus]

This conversation has gone to the dogs, but I suppose that was inevitable with the givens...

I agree that the direct downwind faster than wind is "slightly" unrelated subject.
But they have quite a bit in common.
Both are based on videos made by Derek (Veritasium) and both based on wrongly understanding of what energy is and ignoring completely energy storage.

For Blackbird the pressure differential energy storage was completely ignored and it is the thing allowing that vehicle to exceed wind speed.
For the transmission line the line capacitance was completely ignored and then the effects of that were misinterpreted as electrical energy not being delivered by electrons (charged particles) traveling through the wire.

[gnuarm]

This conversation has gone to the dogs, but I suppose that was inevitable with the givens...

I agree that the direct downwind faster than wind is "slightly" unrelated subject.
But they have quite a bit in common.

The only thing they have in common is that you take a stance which shows you fail to understand an issue, then you weasel around without actually ever completing a line of thought and want to blame everything on effects that are essentially "invisible" and extremely hard to measure. 

I know that was true of the wind car.  I didn't bother to read your effluent on this issue because I quickly recognized the MO. 

[electrodacus]

I agree that the direct downwind faster than wind is "slightly" unrelated subject.
But they have quite a bit in common.

The only thing they have in common is that you take a stance which shows you fail to understand an issue, then you weasel around without actually ever completing a line of thought and want to blame everything on effects that are essentially "invisible" and extremely hard to measure. 

I know that was true of the wind car.  I didn't bother to read your effluent on this issue because I quickly recognized the MO.
[/quote]

All you need to convince me is provide an equation describing the available wind power to Blackbird.
There seems to be a lot of experts but no equation is ever provided.
You (many) claim you understand the subject but are unable to provide the equation.
Yes air molecules are invisible to human eyes and the electrons even more so but there are people that understand those exist and are able to make correct predictions.

So if you want to contradict me please provide the answer to most basic question:  What is the equation describing the available wind power to Blackbird witch is the same as for any other wind powered vehicle that travels directly downwind and is also valid for directly upwind.
Once you provide that equation is super easy to test if it makes the correct predictions.

[PlainName]

All you need to convince me is provide an equation describing the available wind power to Blackbird.

Pw = (0.5 * air density * area * (wind speed - vehicle speed + wash speed)³) - Pp

where:
wash speed = velocity of air being pushed back by the propeller
Pp = power required to turn the propeller

Any equation that ignores the propeller (which is a pretty big part of the entire thing, you know!) is obviously missing something and not appropriate.

[electrodacus]

All you need to convince me is provide an equation describing the available wind power to Blackbird.

Pw = (0.5 * air density * area * (wind speed - vehicle speed + wash speed)³) - Pp

where:
wash speed = velocity of air being pushed back by the propeller
Pp = power required to turn the propeller

Any equation that ignores the propeller (which is a pretty big part of the entire thing, you know!) is obviously missing something and not appropriate.

The question that I asked was Wind power available to vehicle as vehicle is powered by wind power only.
The propeller itself is powered by wind so whatever contribution the propeller makes can not be added to wind power as it is already powered by the wind.
I did not asked about the Power available to vehicle to accelerate as that is not just wind power but after vehicle starts to move is wind power + power provided by the energy storage.

If you want to think vehicle has no energy storage available then it will be nothing other than wind power available and so vehicle could not exceed wind speed.

Take the first fraction of a second for example when vehicle is stationary and will just start to move
Wind speed = 6m/s
vehicle weight = 10kg
area = 1m^2

P_w = 0.5 * air density * area * (wind speed - vehicle speed)³

Say this wind power is split this way (the way it is split will depend on your wheel to propeller gear selection and propeller pitch angle and propeller design)
50% will be used to accelerate the vehicle and 50% used to power the propeller and say proeller is 65% efficient.

Say the integration time interval for this finite analysis calculation is 1 millisecond = 0.001 seconds
Then in this initial first step

P_W = 0.5 * 1.2 * 1 * (6-0)³ = 129.6W
But only 50% of this will be used to accelerate the vehicle so 64.8W and so after this first 1ms the vehicle has gained 64.8mWs = 64.8mJ
Then the other 60% at 65% efficiency will be 129.6W * 0.5 * 0.65 = 42.12W net at propeller
You consider this stored energy and add in next step to the Potential wind energy so currently potential wind energy is
(0.5 * mass * w²) - (0.5 * mass * v²)  = 0.5 * 10 * 6² = 180Ws

So a sail only vehicle will accelerate faster as it will not need to provide 50% of wind power to propeller but the Potential wind energy will drop as vehicle accelerates
On the Blackbird significant part of wind power is diverted to propeller and that pushes back creating higher pressure (sort of like increasing equivalent wind speed relative to vehicle) and so potential wind energy will decrease much slower in the initial acceleration part where there is a lot of wind power available.


In my video I use vehicle speed steps of 0.01m/s instead of time for better resolution with less steps.

In any case the main point is that vehicle (any wind powered vehicle) has just the wind power provide by the formula I mentioned and in the special case of the Blackbird part of the energy is used to power the propeller with the remaining accelerating the vehicle.
If there was no energy storage like for example air was not compressible then all the power you diverted to propeller will immediately push the vehicle.
So say vehicle was traveling through water (non compressible fluid) instead of trough air.
Then out of "Wind" power available half will accelerate the vehicle and the other half go to propeller and say propeller was 100% efficient that will also push the vehicle with the other half so total 100% of available power will accelerate the vehicle but nothing is stored.
With air which is compressible (elastic type of storage like a spring or repulsion forces between electrons) when you send half the power to propeller and say again 100% efficient propeller you get less than that half in push power as air compresses and some of the energy is stored in pressure differential instead of as vehicle kinetic energy keeping the vehicle a longer time at lower speed and so give it a chance to store energy in that pressure differential.
As vehicle picks up speed more and more of the acceleration is contributed from the stored pressure differential and less provided by the wind.

That is how the treadmill vehicle can drive against the motion of the treadmill surface because while you keep the vehicle in place the propeller builds up pressure differential (low pressure in front and high pressure in the back)  and so when you let go that pressure differential is what pulls and pushes the vehicle forward and all energy that is not needed for acceleration and friction is put back by the propeller.
That treadmill vehicle is a much better experimental case as everything is much more controllable (fairly constant treadmill speed) and zero wind speed as it is indoor.
With any high speed camera even 60 or 120FPS you can see when video from the side that vehicle acceleration rate decreases meaning it will get to a point where it will stop accelerating and you can fairly precisely calculate what that time will be and you can also calculate the total stored energy if you know vehicle weight and friction losses.   

[Naej]

All you need to convince me is provide an equation describing the available wind power to Blackbird.

Pw = (0.5 * air density * area * (wind speed - vehicle speed + wash speed)³) - Pp

where:
wash speed = velocity of air being pushed back by the propeller
Pp = power required to turn the propeller

Any equation that ignores the propeller (which is a pretty big part of the entire thing, you know!) is obviously missing something and not appropriate.

The question that I asked was Wind power available to vehicle as vehicle is powered by wind power only.

It's not a wind turbine, it's a propeller.
You'd use a wind turbine into the wind, not dead wind.

So the question you should ask is what's the force propelling the car for a given energy consumption.
With a mass flow of Q, and efficiency of 1, the energy consumption is 1/2*Q*Delta V^2; the momentum given to the car is Q*Delta V.
If Q is large (a big propeller), you obtain a high ratio between the 2, and a good efficiency overall.
Power is of course taken from the wheels.

[SiliconWizard]

Getting off-topic here, but yes, "interestingly", what we commonly call "wind turbines" these days, in the common green vocabulary, are not really turbines.

[PlainName]

All you need to convince me is provide an equation describing the available wind power to Blackbird.

Pw = (0.5 * air density * area * (wind speed - vehicle speed + wash speed)³) - Pp

where:
wash speed = velocity of air being pushed back by the propeller
Pp = power required to turn the propeller

Any equation that ignores the propeller (which is a pretty big part of the entire thing, you know!) is obviously missing something and not appropriate.

The question that I asked was Wind power available to vehicle as vehicle is powered by wind power only.
The propeller itself is powered by wind so whatever contribution the propeller makes can not be added to wind power as it is already powered by the wind.
I did not asked about the Power available to vehicle to accelerate as that is not just wind power but after vehicle starts to move is wind power + power provided by the energy storage.

I gave you exactly what you asked for. The propeller power is taken from the wheels and reduces the power available from the wind, but in turn it provides thrust.

The propeller does not take power from the wind nor provide drive to the wheels. If you think it does then that explains your inability to understand what's going on. Or inability to understand equations, but similar conclusion.

[electrodacus]

It's not a wind turbine, it's a propeller.
You'd use a wind turbine into the wind, not dead wind.

So the question you should ask is what's the force propelling the car for a given energy consumption.
With a mass flow of Q, and efficiency of 1, the energy consumption is 1/2*Q*Delta V^2; the momentum given to the car is Q*Delta V.
If Q is large (a big propeller), you obtain a high ratio between the 2, and a good efficiency overall.
Power is of course taken from the wheels.

Yes it is not a wind turbine but the propeller can only be powered by the wind and stored energy (with is actually the case and was ignored).
You need to ask what is the power available to propel the vehicle. Asking what the force alone is may get you to wrong conclusions.

You can not take power from the wheels.  What you call power from the wheels can only be from wind power or from stored energy like from pressure differential or vehicle kinetic energy or a combination or wind power and power from stored energy.

I think pressure differential energy storage is difficult for people to understand so here is an alternative model.
A sail vehicle that has an electrical generator at the back wheels and say a capacitor or rechargeable battery and motor on the front wheels (propeller replacement).

So initially when starting you have say an ideal sail (they are very close anyway for direct down wind).
So wind power available is 0.5 * air density * sail area * (wind speed - vehicle speed)³
Say wind power is 130W initially
If you do not take any energy from the generator all 130W will be available to accelerate the vehicle (increase vehicle kinetic energy).
If you take 50W at the generator wheels then only difference of 80W is available to accelerate the vehicle.
If you have no energy storage device just put this 50W at 100% efficiency in to front motor wheels then you are back to 130W for acceleration and it will not make sense to do that.
But if you have a supercapacitor or rechargeable battery you can put say 10W in to motor and 40W in to battery.
This way vehicle will spend more time at lower speed as it accelerates slower with just 90W (80+10) but as vehicle gets up to speed there is less and less wind power available so the only thing that still accelerates the vehicle are those 10W coming from the battery and powering the motor.

Hope you understand that no vehicle powered only by wind can exceed wind speed unless it has an energy storage device where it stores energy than is then later used to accelerate the vehicle for a limited amount of time above wind speed.
Any vehicle that is wind powered driving directly downwind without an energy storage device can not exceed wind speed as that will violate the energy  conservation law.

[electrodacus]

I gave you exactly what you asked for. The propeller power is taken from the wheels and reduces the power available from the wind, but in turn it provides thrust.

The propeller does not take power from the wind nor provide drive to the wheels. If you think it does then that explains your inability to understand what's going on. Or inability to understand equations, but similar conclusion.

The thrust that propeller provides can only be smaller than the one wind will have provided if you did not take that energy from the wheels.

The only (and I mean only) energy source is the wind as this is a wind powered vehicle.  There is no such thing as ground power or power from the wheels.
Without adding an energy storage device the vehicle can not exceed wind speed as it is seen for any sail only vehicle.
The propeller is not just a propulsion device but it is also an energy storage device when used in air (a compressible fluid).

Your equation includes "wash speed" can you let me know what that is in an example ? How do you calculate that ?
Also you do realize that Wind power will be zero before vehicle gets to wind speed in your equation for any wash speed higher than zero.
Subtracting the propeller power (more correctly power you take at the wheel to provide the propeller if propeller is not 100% efficient) will just show the power available for accelerating the vehicle and not wind power available to vehicle.


So as an example wind speed 6m/s and afrea 1m² to keep things simple

Vehicle speed = 0
P_w = 0.5 * 1.2 * 1 * (6-0)³ = 129.6W
Vehicle speed = 3m/s  (half the wind speed)
P_w = 0.5 * 1.2 * 1 * (6-3)³ = 16.2W   (so 8x less wind power already)
Vehicle speed = 6m/s
P_w = 0.5 * 1.2 * 1 * (6-6)³ = 0W

Now your equation will provide the same for wash speed = 0 and lower values for wash speed higher than zero.
As for subtracting propeller power again all the values will be lower than the ones above.

[gnuarm]

I agree that the direct downwind faster than wind is "slightly" unrelated subject.
But they have quite a bit in common.

The only thing they have in common is that you take a stance which shows you fail to understand an issue, then you weasel around without actually ever completing a line of thought and want to blame everything on effects that are essentially "invisible" and extremely hard to measure. 

I know that was true of the wind car.  I didn't bother to read your effluent on this issue because I quickly recognized the MO.

All you need to convince me is provide an equation describing the available wind power to Blackbird.
There seems to be a lot of experts but no equation is ever provided.
You (many) claim you understand the subject but are unable to provide the equation.
Yes air molecules are invisible to human eyes and the electrons even more so but there are people that understand those exist and are able to make correct predictions.

So if you want to contradict me please provide the answer to most basic question:  What is the equation describing the available wind power to Blackbird witch is the same as for any other wind powered vehicle that travels directly downwind and is also valid for directly upwind.
Once you provide that equation is super easy to test if it makes the correct predictions.

Lol!  It is YOU who has failed.  You have mis-attributed the quotes of your words to me!

I don't care about convincing you of anything.  Your failure is self-sustaining and you will live a rich, full life believing you are right.  So, enjoy.   

[Alex Eisenhut]

What if there's lightning inside a tornado? Will the electons move faster if the lightning is going in the same direction as the tornado?

[electrodacus]

What if there's lightning inside a tornado? Will the electons move faster if the lightning is going in the same direction as the tornado?

What ?
I guess this is related to the hairdryer question where the fan cooled the heating wires which meant  lower resistance and thus higher current as voltage is the same.
Higher current means more electrons traveling through the same cross section area in a unit of time.
Not quite sure what part you disagree with?  Turn on the fan on the hairdryer and you will see the heating elements glowing in visible spectrum meaning higher temperature and depending on what material the heating element is made out of is likely resistance will increase with increased temperature as the metal lattice will vibrate at higher frequency.

[Naej]

Getting off-topic here, but yes, "interestingly", what we commonly call "wind turbines" these days, in the common green vocabulary, are not really turbines.

"Turbine: a machine for producing continuous power in which a wheel or rotor, typically fitted with vanes, is made to revolve by a fast-moving flow of water, steam, gas, air, or other fluid."
Is it too slow for you???

[aetherist]

What if there's lightning inside a tornado? Will the electons move faster if the lightning is going in the same direction as the tornado?

Tornados are indeed electric machines.
But i doubt that the electricity in a tornado has much to do with my electons.
It involves electrons not my electons. The electrons are the usual kinds – free solitary electrons -- & ions (negative & positive).
My electons liv on conductors, eg wires.

[electrodacus]

Lol!  It is YOU who has failed.  You have mis-attributed the quotes of your words to me!

I don't care about convincing you of anything.  Your failure is self-sustaining and you will live a rich, full life believing you are right.  So, enjoy.   

All evidence points to the fact that energy travels through wires.
There are no invisible hard to measure effects to prove that.
Inside a charged capacitor (potential energy storage device) you have a constant electric field.
If you were to measure that field (invisible but can be measured or calculated) you will see that as capacitor gets discharged (electrons traveling through a conductor from the negatively charged plate to the negatively charged one) the field strength decreases and you see electromagnetic energy being radiated out of the conductor not the other way around. Also the electromagnetic energy release will happen delayed due to the thermal storage capacity of the condutor.
All this is fact and can be measured.

[Naej]

It's not a wind turbine, it's a propeller.
You'd use a wind turbine into the wind, not dead wind.

So the question you should ask is what's the force propelling the car for a given energy consumption.
With a mass flow of Q, and efficiency of 1, the energy consumption is 1/2*Q*Delta V^2; the momentum given to the car is Q*Delta V.
If Q is large (a big propeller), you obtain a high ratio between the 2, and a good efficiency overall.
Power is of course taken from the wheels.

Yes it is not a wind turbine but the propeller can only be powered by the wind and stored energy (with is actually the case and was ignored).
You need to ask what is the power available to propel the vehicle. Asking what the force alone is may get you to wrong conclusions.

You can not take power from the wheels.  What you call power from the wheels can only be from wind power or from stored energy like from pressure differential or vehicle kinetic energy or a combination or wind power and power from stored energy.

I think pressure differential energy storage is difficult for people to understand so here is an alternative model.
A sail vehicle that has an electrical generator at the back wheels and say a capacitor or rechargeable battery and motor on the front wheels (propeller replacement).

So initially when starting you have say an ideal sail (they are very close anyway for direct down wind).
So wind power available is 0.5 * air density * sail area * (wind speed - vehicle speed)³
Say wind power is 130W initially
If you do not take any energy from the generator all 130W will be available to accelerate the vehicle (increase vehicle kinetic energy).
If you take 50W at the generator wheels then only difference of 80W is available to accelerate the vehicle.
If you have no energy storage device just put this 50W at 100% efficiency in to front motor wheels then you are back to 130W for acceleration and it will not make sense to do that.
But if you have a supercapacitor or rechargeable battery you can put say 10W in to motor and 40W in to battery.
This way vehicle will spend more time at lower speed as it accelerates slower with just 90W (80+10) but as vehicle gets up to speed there is less and less wind power available so the only thing that still accelerates the vehicle are those 10W coming from the battery and powering the motor.

Hope you understand that no vehicle powered only by wind can exceed wind speed unless it has an energy storage device where it stores energy than is then later used to accelerate the vehicle for a limited amount of time above wind speed.
Any vehicle that is wind powered driving directly downwind without an energy storage device can not exceed wind speed as that will violate the energy  conservation law.

The power is taken from the wheel in the sense that there is a significant friction on the tires, and this is the key for understanding how the car accelerates.
At the same time there is larger force forward given by the propeller (when you accelerate).
As I said before, it's a propeller not a turbine.
If wind speed+1m/s=vehicle speed, you can take 130 W from the wheel and get a large thrust from the propeller.
For example, if the propeller gets 10 kg/s of air, it can accelerate it to 2.7 m/s and get a thrust of 27 N.
If the vehicle speed is more than 5 m/s this is more than tire friction and your vehicle accelerate.
You get a large torque, which is why the vehicle is shaped like this.

Energy conservation is correct in a closed system. If you don't define the system, you can easily say wrong things, like here. And if you don't define the reference frame, ditto.
Bottom line is: both the atmosphere and the Earth are big, so there's a huge amount of energy in wind and if you neglect the annoying drag, you can go as fast as you want.

There are plenty of things going faster than the wind.
For example:
- a glider, here at 880 km/h in 104 km/h wind 
- all wind turbines.

It works in the same way as sailing boats which go faster than the wind, you just need to change direction regularly (tacking), and a rotor does this in an almost perfect way.

[PlainName]

I gave you exactly what you asked for. The propeller power is taken from the wheels and reduces the power available from the wind, but in turn it provides thrust.

The propeller does not take power from the wind nor provide drive to the wheels. If you think it does then that explains your inability to understand what's going on. Or inability to understand equations, but similar conclusion.

The thrust that propeller provides can only be smaller than the one wind will have provided if you did not take that energy from the wheels.

The only (and I mean only) energy source is the wind as this is a wind powered vehicle.  There is no such thing as ground power or power from the wheels.

OK, I'll allow that the way I wrote that could be misinterpreted. Obviously, the only source of power is the wind, and what I meant was that the wind is not driving the wheels via the propeller - the wind is pushing the vehicle which turns the wheels that drive the propeller.

Nevertheless, you asked what power from the wind was available to push the vehicle, and that formula tells you - it is the wind power acting on the surface MINUS the power necessary to turn the propeller. I am still surprised that you can't grasp that that power to turn the prop is taken from the power available to push, reducing the apparent pushing power.

The only (and I mean only) energy source is the wind as this is a wind powered vehicle.  There is no such thing as ground power or power from the wheels.

I have no idea why you think this equation shows any power source other than the wind. I have explicitly and at length told you that the wind is the only source, and said that several times.

Your equation includes "wash speed" can you let me know what that is in an example ?

It is the thrust from the propeller. I can't believe that now we have to explain to you how an airplane manages to fly. Do you really need to be told what 'thrust from a propeller' means? Really?

How do you calculate that ?

It will depend on the gearing to the prop, the pitch, the speed of the vehicle, etc. However, that is not important or relevant - you asked for a formula showing the available power and that is what you got. If you want the know the maximum speed possible then we would then need to work out the details of the prop and do some calculations, but that isn't what you asked so it's not what you got.

Subtracting the propeller power (more correctly power you take at the wheel to provide the propeller if propeller is not 100% efficient) will just show the power available for accelerating the vehicle and not wind power available to vehicle.

Well, at this point one has to ask "What the  hell is the question you're asking!?!?" Clearly, the total power available is the wind acting on the surface, which is the equation you provided. There is no other power, so it is that which provides for the acceleration and everything else.

Also, I think you've failed to remember that the test vehicle had the prop blades feathered until it reached close to wind speed, at which point they were manually adjusted to provide appropriate thrust. I think you should consider that a significant clue.

However, what is very clear is that even when you get precisely what you ask for, you don't live up to your promise. There is no point or use in discussing anything with you because you are blind and immune to anything except whatever your mind has made up.

[electrodacus]

The power is taken from the wheel in the sense that there is a significant friction on the tires, and this is the key for understanding how the car accelerates.
At the same time there is larger force forward given by the propeller (when you accelerate).
As I said before, it's a propeller not a turbine.
If wind speed+1m/s=vehicle speed, you can take 130 W from the wheel and get a large thrust from the propeller.
For example, if the propeller gets 10 kg/s of air, it can accelerate it to 2.7 m/s and get a thrust of 27 N.
If the vehicle speed is more than 5 m/s this is more than tire friction and your vehicle accelerate.
You get a large torque, which is why the vehicle is shaped like this.

Energy conservation is correct in a closed system. If you don't define the system, you can easily say wrong things, like here. And if you don't define the reference frame, ditto.
Bottom line is: both the atmosphere and the Earth are big, so there's a huge amount of energy in wind and if you neglect the annoying drag, you can go as fast as you want.

There are plenty of things going faster than the wind.
For example:
- all wind turbines.

It works in the same way as sailing boats which go faster than the wind, you just need to change direction regularly (tacking), and a rotor does this in an almost perfect way.

You are a smart guy based on the other comments I saw from you.

I'm fairly bad at explaining things but I will try my best.

Let's start with the simplest wind powered vehicle just wheels and a sail driving directly downwind (very important it is directly downwind as even a sail vehicle can exceed wind speed if it drives at an angle).
 
I guess you will agree that wind power available to this vehicle (ideal case no friction involved) is 0.5 * air density * area * (wind speed - vehicle speed)³
Highest wind potential energy is when vehicle speed relative to the ground is zero.
This wind potential energy can be all converted to kinetic energy in ideal case so ideal vehicle speed can get at most at wind speed.

Now no matter how you modify the vehicle the air particles can only interact by colliding with equivalent area of the vehicle.

So now let just say vehicle is at half the wind speed and just 16.2W of wind power is available to this ideal vehicle no friction.
You can use this 16.2W to increase the vehicle kinetic energy (increase vehicle speed) or you can decide to take that extract energy from the wheels let say to power a 16.2W incandescent light bulb.
In this case since you take 16.2W from the wheels to power the 16.2W lamp the vehicle will no longer accelerate and just maintain the same speed (half the wind speed in this example).
Now you can replace that incandescent lamp with whatever you want. Can you make the vehicle accelerate faster than it already did before deciding to take those 16.2W from the generator wheels ?
Say you install an electric driven propeller and supply those 16.2W to that and also let say the propeller is 100% efficient. Can you get more than 16.2W worth of thrust ?

I hope you agree you can not get more power out than you get in.
Somehow people think either propeller's or gearboxes are magical devices that can output more power than they get in.
Power you take at the wheel is wind power so taking that subtracts from wind power available to vehicle to accelerate.
Without adding an energy storage device no vehicle can exceed with speed powered by the wind.   

[electrodacus]

Well, at this point one has to ask "What the  hell is the question you're asking!?!?" Clearly, the total power available is the wind acting on the surface, which is the equation you provided. There is no other power, so it is that which provides for the acceleration and everything else.

Also, I think you've failed to remember that the test vehicle had the prop blades feathered until it reached close to wind speed, at which point they were manually adjusted to provide appropriate thrust. I think you should consider that a significant clue.

However, what is very clear is that even when you get precisely what you ask for, you don't live up to your promise. There is no point or use in discussing anything with you because you are blind and immune to anything except whatever your mind has made up.

Both my equation and the one you provides shows that vehicle can not exceed wind speed unless and energy storage device is included.
Just put some real numbers in the equation you provided and see for yourself that your equations shows no wind power above wind speed.

[PlainName]

Both my equation and the one you provides shows that vehicle can not exceed wind speed unless and energy storage device is included.

Rubbish. The one you provided shows there is zero power at wind speed, but the proper version that I provided doesn't show that. It does show that power will reach zero but not the speed at which that happens. That will be dependent on how much power is taken for the prop and what thrust the prop provides.

From the equation as it stands, you cannot know if the vehicle will even reach wind speed or exceed it. To suggest otherwise means you are pre-judging based on only your bias, without thinking what the equation actually says.

[electrodacus]

Both my equation and the one you provides shows that vehicle can not exceed wind speed unless and energy storage device is included.

Rubbish. The one you provided shows there is zero power at wind speed, but the proper version that I provided doesn't show that. It does show that power will reach zero but not the speed at which that happens. That will be dependent on how much power is taken for the prop and what thrust the prop provides.

From the equation as it stands, you cannot know if the vehicle will even reach wind speed or exceed it. To suggest otherwise means you are pre-judging based on only your bias, without thinking what the equation actually says.

This is the equation you provided
P_w = (0.5 * air density * area * (wind speed - vehicle speed + wash speed)³) - P_p

You added "wash speed" and P_p
If both values are zero you get zero wind power at vehicle speed equals wind speed.
If "wash speed" is any value higher than zero then wind power will be zero before vehicle even gets to wind speed and the same happens with P_p

Just use 6m/s for wind speed and same for vehicle speed and area can be 1² to keep calculation simple. Add any values you think are realistic for P_p and "wash speed" and let me know what the wind power is is when vehicle speed equals wind speed.

[PlainName]

If both values are zero you get zero wind power at vehicle speed equals wind speed.

Yes, and...?

[Quick diversion: they won't both be zero because the thing is moving, hence turning the wheels, hence sucking power, etc.]

But let's just recap what this is about:

All you need to convince me is provide an equation describing the available wind power to Blackbird.

That's what you got. No more, no less. You can try the faithful distraction technique of diving into irrelevant details and hope someone will start arguing those, but that doesn't change anything. The equation is either good or it isn't. Plug in whatever values you like, but they're not going to change what the equation is saying.

So, what is wrong with it? It includes the important stuff yours conveniently left out - there is a big propeller sucking power by causing drag on the wheels, so even if you don't like this equation, your version is even worse.

Add any values you think are realistic for Pp and "wash speed" and let me know

Completely irrelevant diversion. Settle on the equation and then you can think about values. You don't change things to suit the result you've already decided upon.